A systematic approach for multidimensional, closed-form analytic modeling:Minority electron mobilities in Ga1-xAlxAs heterostructures

A significant, practical challenge, which arises in developing computationa lly efficient physical models for use in computer simulations of microelect ronic and optoelectronic devices (for example, transistors in digital cellu lar phones and lasers in optical networks, respectively), is to represent v ast amounts of numerical data for transport properties in two or more dimen sions in terms of closed form analytic expressions. In this paper, we prese nt a general methodology to achieve the above goal for a class of numerical data in a bounded two-dimensional space. We then apply this methodology to obtain a closed-form analytic expression for the minority electron mobilit ies at 300 K in p-type Ga1-xAlxAs as functions of the acceptor density N-A between 10(16) cm(-3) and 10(20) cm(-3) and the mole fraction of AlAs x bet ween 0.0 and 0.3. This methodology and its associated principles, strategie s, regression analyses, and graphics are expected to be applicable to other problems beyond the specific case of minority mobilities addressed in this paper.